Ricci flow singularity evidence audit

Family 351: Scalar curvature and finite-time Ricci-flow singularities. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometric flow researchers can distinguish scalar-curvature monitoring sufficient for extension in dimension four from failure in higher dimensions.

Applicability and commercial boundary

Dimension and smooth closed-domain assumptions matter. A sampled bounded scalar field is not a uniform all-time bound or a numerical continuation certificate.

Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

Next verification action

Extract the higher-dimensional example and specify which diagnostics a finite solver can legitimately observe.

Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup.